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described as the Mathematic of sense, Mathematic as Music of
the reason? Thus the musician feels Mathematic, the mathe-
matician thinks Music - Music the dream, Mathematic the
working life - each to receive its consummation from the other
when the human intelligence, elevated to its perfect type, shall
shine forth glorified in some future Mozart-Dirichlet or Beet-
hoven-Gauss - a union already not indistinctly foreshadowed
in the genius and labours of a Helmholtz!'
Sylvester loved life, even when he was forced to fight it, and
if ever a man got the best that is in life out of it, he did. He
gloried in the fact that the great mathematicians, except for
what may he classed as avoidable or accidental deaths, have
been long-lived and vigorous of mind to their dying days. In
his presidential address to the British Association in 1869 he
called the honour roll of some of the greatest mathematicians
of the past and gave their ages at death to bear out his thesis
that *... there is no study in the world which brings into more
harmonious action all the faculties of the mind than [mathe-
matics], ... or, like this, seems to raise them, by successive
steps of initiation, to higher and higher states of conscious
intellectual being. ,.. The mathematician lives long and lives
young; the wings of the soul do not early drop off, nor do its
pores become clogged with the earthy particles blown from the
dusty highways of vulgar life.*
Sylvester was a living example of his own philosophy. But
even he at last began to bow to time. In 1893 - he was then
seventy-nine - his eyesight began to fail, and he became sad and
discouraged because he could no longer lecture with his old
enthusiasm. The following year he asked to be relieved of the
more onerous duties of his professorship, and retired to live,
lonely and dejected, in London or at Tunbridge Wells. All his
brothers and sisters had long since died, and he had outlived
most of his dearest friends.
But even now he was not through. TTip mind was still vigor-
ous, although he himself felt that the keen edge of his inventive-
ness was dulled for ever. Late in 1896, in the eighty-second year
of his age, he found a new enthusiasm in a field which had
alwa3*s fascinated him, and he blazed up again over the theory